We present feedback control methodologies for the stabilization of nonlinear collective dynamics. The proposed controllers circumvent the curse of dimensionality associated to dynamic programming of large-scale nonlinear dynamics by means of different structural assumptions on the nonlinearity and the associated Hamilton-Jacobi-Bellman equation. We explore a power series expansion method, and a state-dependent Riccati equation approach. The proposed designs are studied for a relaxed optimal power flow model, and for binary interactions arising in opinion and consensus dynamics.